U.S. Pat. No. 7,440,814 describes a method for auto-calibration of a tool in a single point turning machine used for manufacturing in particular ophthalmic lenses, method in which a test piece of predetermined geometry is cut with the tool and probed to obtain probe data. The method uses the probe data to mathematically and deterministically identify the necessary tool/machine corrections in two directions (X, Y) or direction directions (X, Y, Z) of the machine.
In particular, the method first describes a method for calibration of the tool in the X and Y directions (named 2D calibration concept). The method comprises the following steps:                cut a predefined circular groove in a test piece, the groove defining a rotationally symmetrical geometry requiring both positive and negative tool contact angles;        probe the test piece and in particular the curved section line of the circular groove and store the probe data obtained;        execute best fit analysis of probe data to determine best fit of theoretical test piece geometry through the actual geometry of the test piece;        determine X-offset by comparing actual to theoretical results;        determine Y-offset by comparing actual to theoretical results;        execute best fit analysis of probe data to determine best fit circle through a general tool tip geometry;        analyse probe data to determine tool waving waviness errors in the Y-direction relative to a slope of a tangent angle between tool tip and test piece;        store results of above analyses in appropriate memory register and/or data files; and        use results by appropriately controlling the machine's X and Y axes to correct for X and Y axes.        
Next, the method describes a method for calibration of the tool in the X, Y and Z directions (named 3D calibration concept). The method comprises the following steps:                cut a predefined asymmetrical surface along two horizontal axes in a test piece, the surface defining a rotationally asymmetrical geometry;        probe the test piece and store the probe data obtained;        analyse probe data to determine general tool tip geometry, distance from center of best fit tool tip radius to center of lens rotation (in X-direction) and Y-errors relative to slope of tangent angle between the turning tool and the test piece;        probe test piece while rotating it and store probe data;        analyse probe data to determine Z-direction distance of cutting edge of the tool to center of axis of work rotation;        store results of above analyses; and        use results by appropriately controlling the machine's X, Y and Z axes to correct for X, Y and Z axes.        
The method described above thus allows determining actual location of the tool at least in the X and Y directions, and optionally in the Z direction, relative to the machine, and correcting the position of the tool in the machine.